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Date May 2021 Marks available 1 Reference code 21M.1.SL.TZ2.7
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 2
Command term Suggest Question number 7 Adapted from N/A

Question

A large school has students from Year 6 to Year 12.

A group of 80 students in Year 12 were randomly selected and surveyed to find out how many hours per week they each spend doing homework. Their results are represented by the following cumulative frequency graph.

This same information is represented by the following table.

There are 320 students in Year 12 at this school.

Find the median number of hours per week these Year 12 students spend doing homework.

[2]
a.

Given that 10% of these Year 12 students spend more than k hours per week doing homework, find the value of k.

[3]
b.

Find the value of p and the value of q.

[4]
c.

Estimate the number of Year 12 students that spend more than 15 hours each week doing homework.

[3]
d.

Explain why this sampling method might not provide an accurate representation of the amount of time all of the students in the school spend doing homework.

[1]
e.i.

Suggest a more appropriate sampling method.

[1]
e.ii.

Markscheme

evidence of median position             (M1)

40 students

median =14 (hours)           A1

 

[2 marks]

a.

recognizing there are 8 students in the top 10%             (M1)

72 students spent less than k hours             (A1)

k=18 (hours)           A1

 

[3 marks]

b.

15 hours is 60 students  OR  p=60-4             (M1)

p=56           A1

21 hours is 76 students  OR  q=8076  OR  q=8045616             (A1)

q=4           A1

 

[4 marks]

c.

20 of the 80 students OR 14 spend more than 15 hours doing homework             (A1)

2080=x320  OR  14×320  OR  4×20             (A1)

80 (students)           A1

 

[3 marks]

d.

only year 12 students surveyed OR amount of homework might be different for different year levels        R1

 

[1 mark]

e.i.

stratified sampling OR survey students in all years     R1

 

[1 mark]

e.ii.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.
[N/A]
e.i.
[N/A]
e.ii.

Syllabus sections

Topic 4—Statistics and probability » SL 4.1—Concepts, reliability and sampling techniques
Show 29 related questions
Topic 4—Statistics and probability » SL 4.2—Histograms, CF graphs, box plots
Topic 4—Statistics and probability

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